Scanning Probe Microscopy (SPM) is a field of microscopy that encompasses a variety of techniques that probe the surface characteristics of matter on the micrometer to nanometer scales. These techniques are used in creating topography models of samples as well as maps of various physical or chemical properties detectable at the surface of a sample including composition, adhesion, friction, viscoelasticity and elastic modulus, electrostatic forces, magnetic forces, piezoelectric response, and surface potential distribution properties. These techniques are used to study nanometer-scale processes at surfaces, transport in electronic materials, self assembled nanostructures, block copolymers, ferroelectric and magnetic domain interactions, crack tip plasticity, variations in surface adhesion or hardness, and a variety of nanotube properties. Other applications include identification of contaminants, mapping of components in composite materials, detection of trapped charges, testing of electrical continuity, and failure analysis.
Common to SPM techniques is the use of a probe mounted to the free end of a cantilever arm in communication with a detector that measures deflection of the cantilever arm caused by interaction between the probe tip and the sample. The deflection data is processed in accordance with algorithms that produce models of surface topology and other features and properties of matter. In some SPM techniques, the probe tip comes in contact with the sample, either continuously or intermittently. In one form of contact SPM, the topography is measured by rastering the probe tip while in continuous contact with the sample surface to produce a high-resolution topographic map. In another form of contact SPM, the probe tip is in intermittent contact with the sample surface thereby reducing surface shear forces that can damage soft samples and decrease image resolution. Intermittent contact SPM also allows imaging of samples that are difficult to image by other contact SPM techniques.
In non-contact SPM techniques, the probe tip is maintained at a distance from the surface of the sample. Examples of SPM techniques that utilize non-contact scanning include Electric Force Microscopy (EFM), Scanning Impedance Microscopy (SIM), and Scanning Surface Potential Microscopy (SSPM).
SSPM is based on nulling the first harmonic of tip-surface force induced by tip AC bias. Nulling is achieved when the tip DC bias offset is equal to the surface potential, thus providing the local potential map. SSPM is characterized by the use of two different types of scans of the sample. In the first scan, a grounded probe tip collects surface topography data through intermittent contact with the sample. The second scan retraces the path of the first scan but maintains the probe tip at a distance from the surface of the sample. During the second scan, the probe tip is driven by an AC bias applied directly to the probe tip. The bias results in the periodic application of force at the bias frequency, which amplitude and phase depends on, in large part, driving frequency, tip surface capacitance and driving amplitude. In this manner, SSPM allows for the determination of local surface potential, visualization of electroactive grain boundaries, spatially resolved resistance and capacitance measurements of individual interfaces, and transport properties of samples.
A similar double scan approach is used in EFM and SIM. EFM involves the detection of the amplitude, phase or frequency shift of a DC-biased, mechanically oscillated probe tip which measures electrostatic charges and surface potential distribution properties of the sample surface.
SIM is based on the detection of phase and amplitude changes of a DC-biased, oscillated probe tip in which the cantilever oscillations are induced by a lateral AC bias applied across the sample. This technique allows imaging of resistive and capacitive barriers at the interfaces and can be used to determine local interface capacitance. The bias induces oscillations in surface potential resulting in the periodic force acting on the probe tip.
Electrostatic SPM techniques such as EFM, SIM and SSPM have become important tools for the characterization of the electric properties of material on the micron and submicron levels. S. V. Kalinin and D. A. Bonnell, Scanning Probe Microscopy and Spectroscopy: Theory, Techniques and Applications, ed. D. A. Bonnell (Wiley VCH, New York, 2000, p. 205). On grounded surfaces, these techniques provide information on the local potential as determined by, for example, surface composition, ferroelectric polarization and trapped charges. When applied to a laterally biased surface, these techniques can provide information on the local transport properties. These SPM techniques provide a powerful approach for the characterization of local transport properties and failure analysis of nano- and molecular electronic devices.
The effectiveness of these SPM techniques for quantitative nanometer scale imaging is influenced by geometric tip effects. These effects are combined with the surface data collected from the sample to produce a composite image of the surface data convoluted with artifacts of the probe tip used to obtain the image. The altered version of the surface is shown in the smearing of observed potential distributions and cross-talk between potential and topographic images. Z. Y. Li, B. Y. Gu, and G. Z. Yang, Phys. Rev. B 57, 9225 (1998); S. Lanyi, J. Torok, and P. Rehurek, J. Vac. Sci. Technol. B 14, 892 (1996); A. Efimov and S. R. Cohen, J. Vac. Sci. Technol. A 18, 1051 (2000). Thus, an accurate interpretation of the surface data requires the determination of, for example, the tip geometry and electrostatic properties that contribute to the SPM image such as tip-surface contrast transfer. By separating the tip contribution from the experimental data obtained regarding the surface properties of the sample, a more accurate representation of the sample surface can be produced. Accordingly, accurate imaging of potential distributions in active micro- and nanoelectronic devices by SSPM and related non-contact electrostatic SPM techniques requires an understanding of tip geometry and tip-surface contrast transfer.
For small tip-surface separations, the tip geometry can be accounted for through spherical tip approximation, and the corresponding geometric parameters can be obtained from electrostatic force- or force gradient distance and bias dependencies. S. Belaidi, P. Girard, and G. Leveque, J. Appl. Phys. 81, 1023 (1997); L. Olsson, N. Lin, V. Yakimov, and R. Erlandsson, J. Appl. Phys. 84, 4060 (1998). Such a calibration process is often tedious and tip parameters tend to change with time due to mechanical tip instabilities. H. O. Jacobs, H. F. Knapp, and A. Stemmer, Rev. Sci. Instr. 70, 1756 (1999). Alternatively, the tip contribution to measured surface properties can be quantified directly using an appropriate calibration method. F. Robin, H. Jacobs, O. Homan, A. Stemmer, and W. Bxc3xa4chtold, Appl. Phys. Lett. 76, 2907 (2000). If known, a tip-surface transfer function can be used to deconvolute the tip contribution from experimental data and obtain the exact surface potential distribution.
Systems with well defined metal-semiconductor interfaces have been considered as a xe2x80x9cpotential stepxe2x80x9d standard. H. O. Jacobs, P. Leuchtmann, O. J. Homan, and A. Stemmer, J. Appl. Phys. 84, 1168 (1998). However, the presence of surface states and mobile charges significantly affect potential distributions of grounded surfaces. In addition, such a standard is expected to be sensitive to environmental conditions such as humidity, temperature, and other factors. H. Sugimura, Y. Ishida, K. Hayashi, O. Takai, and N. Nakagiri, Appl. Phys. Lett. 80, 1459 (2002).
The applicability of these SPM techniques has been hindered by the lack of reliable standards for electrostatic SPM resolution. While the performance of topographic SPM can be reliably calibrated with calibration gratings, no such standard has been developed for electrostatic measurements. Such a standard is critical for the unambiguous determination of the tip contribution to surface properties, especially on the sub-micron scale. If known, a tip-surface transfer function can be used to deconvolute tip contribution from experimental data and obtain exact surface potential distribution.
The well-defined geometry and stability exhibited by carbon nanotubes have enabled their successful application as scanning probe microscopy probes. H. J. Dai, J. H. Hafner, A. G. Rinzler, D. T. Colbert, R. E. Smalley, Nature 384, 147 (1996); S. Takahashi, T. Kishida, S. Akita, and Y. Nakayama, Jpn. J. Appl. Phys. B 40, 4314 (2001); S. B. Arnason, A. G. Rinzler, Q. Hudspeth, and A. F. Hebard, Appi. Phys. Lett. 75, 2842 (1999); N. Choi, T. Uchihashi, H. Nishijima, T. Ishida, W. Mizutani, S. Akita, Y. Nakayama, M. Ishikawa, and H. Tokumoto, Jpn. J. Appl. Phys. B 39, 3707 (2000). It has not, however, been heretofore recognized that carbon nanotubes can be combined into a tip calibration standard useful as a calibration standard for probe tips in electrostatic SPM.
In accordance with one aspect of the present invention, there is provided a tip calibration standard for calibrating scanning probe microscope probe tips comprising a carbon nanotube structure adapted for characterizing the geometric and electrostatic properties of probe tips used in SPM. In particular embodiments, the standard comprises a metallic or semiconductive, single-wall or multi-wall carbon nanotube disposed on a dielectric surface of a grounded, conductive substrate and in connection with a contact mounted on the substrate.
In accordance with another aspect of the present invention, there is provided a method for calibrating an SPM probe tip mounted on a cantilever arm in communication with a cantilever deflection detector comprising the steps of applying an AC bias to the nanotube of the standard of the present invention, measuring with the detector the cantilever deflection caused by a scan of the AC-biased standard with the probe tip; and converting the cantilever deflection data into probe tip data. This method of SPM probe tip calibration permits simultaneous imaging of the tip geometry and measurement of electrostatic resolution, as well as determining the convolution function for electrostatic SPM. In embodiments in which the nanotube diameter is known, the proportionality coefficient between tip capacitance and the deflection data also can be computed.